A Note on ODEs from Mirror Symmetry

  • A. Klemm
  • B. H. Lian
  • S. S. Roan
  • S. T. Yau
Part of the Progress in Mathematics book series (PM, volume 132)


We give close formulas for the counting functions of rational curves on complete intesection Calabi-Yau manifolds in terms of special solutions of generalized hypergeometric differential systems. For the one modulus cases we derive a differential equation for the Mirror map, which can be viewed as a generalization of the Schwarzian equation. We also derive a nonlinear seventh order differential equation which directly governs the Prepotential.


Modulus Space Yukawa Coupling Elliptic Curve Complete Intersection Elliptic Curf 
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Copyright information

© Birkhäuser Boston 1996

Authors and Affiliations

  • A. Klemm
    • 1
  • B. H. Lian
    • 2
  • S. S. Roan
    • 3
  • S. T. Yau
    • 2
  1. 1.Theory DivisionCERNGeneva, 23Switzerland
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA
  3. 3.Institute of MathematicsAcademia SinicaTaipeiTaiwan

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